$89$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $49$ less than $2$ times the number of away team fans. How many home team and away team fans attended the game?
Explanation: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 89}$ ${x = 2y-49}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${2y-49}$ for $x$ in the first equation. ${(2y-49)}{+ y = 89}$ Simplify and solve for $y$ $ 2y-49 + y = 89 $ $ 3y-49 = 89 $ $ 3y = 138 $ $ y = \dfrac{138}{3} $ ${y = 46}$ Now that you know ${y = 46}$ , plug it back into ${x = 2y-49}$ to find $x$ ${x = 2}{(46)}{ - 49}$ $x = 92 - 49$ ${x = 43}$ You can also plug ${y = 46}$ into ${x+y = 89}$ and get the same answer for $x$ ${x + }{(46)}{= 89}$ ${x = 43}$ There were $43$ home team fans and $46$ away team fans.